Non-Parametric Interval Estimation of Relative Potency for Dilution Assays, Including the Case of Non-Monotone Dosage Response Curves

Interval estimates of the relative potency of two preparations based on data from a dilution assay can be made using an extension of the Mantel-Haenszel procedure, this requiring only the assumption of a monotone dosage-response curve. An assay-design requirement is that dosage levels be equi-spaced logarithmically with a common logarithmic interval for both preparations. By use of ranks the method can be made independent of the scale in which responses are measured. The approach is illustrated using untransformed data, a logarithmic transform, a quantal transform, and a ranking scale. A procedure under which even the monotonicity assumption can be dropped is described and similarly illustrated.